A HYBRID NEWTON METHOD FOR SOLVING BOX CONSTRAINED VARIATIONAL INEQUALITY PROBLEMS VIA THE D-GAP FUNCTION
Ji-Ming Peng 1 2 , Christian Kanzow 3 4 and Masao Fukushima 5 6 ;
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State Key Laboratory of Scienti c and Engineering Computing Institute of Computational Mathematics and Scienti c/Engineering Computing Academic Sinica P.O. Box 2719, Beijing 100080, China e-mail:
[email protected] 3
Institute of Applied Mathematics University of Hamburg Bundesstrasse 55 D-20146 Hamburg, Germany e-mail:
[email protected] 5
Department of Applied Mathematics and Physics Graduate School of Engineering Kyoto University Kyoto 606-01, Japan e-mail:
[email protected] December 30, 1997 A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented. Abstract.
Variational inequality problem, box constraints, D-gap function, Newton's method, unconstrained optimization, global convergence, quadratic convergence.
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2 The research of this author was supported by Project 19601035 of NSFC in China. 4 Current address (October 1, 1997 | September 30, 1998): Computer Sciences Department,
University of Wisconsin | Madison, 1210 West Dayton Street, 53706 Madison, WI; e-mail:
[email protected]. The research of this author was supported by the DFG (Deutsche Forschungsgemeinschaft). 6 The work of this author was supported in part by the Scienti c Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.
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Introduction Let F be a mapping from
